ECE 576 – Power System
Dynamics and Stability
Lecture 16: Governors, Multimachine
Simulations
Prof. Tom Overbye
Dept. of Electrical and Computer Engineering
University of Illinois at Urbana-Champaign
overbye@illinois.edu
1
Announcements
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Exam average was 85
Homework 5 is assigned today; due on April 3
Read Chapter 7
A useful reference is B. Stott, "Power System Dynamic
Response Calculations," Proc. IEEE, vol. 67, pp. 219241
2
IEEEG1
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A common stream turbine model, is the IEEEG1,
originally introduced in the below 1973 paper
In this model K=1/R
Uo and Uc are rate
limits
It can be used to represent
cross-compound units, with
high and low pressure steam
IEEE Committee Report, “Dynamic Models for Steam and Hydro Turbines in Power System Studies,”
Transactions in Power Apparatus & Systems, volume 92, No. 6, Nov./Dec. 1973, pp 1904-15
3
IEEEG1
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Blocks on the right model the various steam stages
About 12% of WECC governors are currently IEEEG1s
Below figures show two test comparison with this
model with one matching well and one not
Image Source: Figs 2-4, 2-6 of IEEE PES, "Dynamic Models for Turbine-Governors in Power System Studies," Jan 2013
4
Deadbands
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Before going further, it is useful to briefly consider
deadbands, with two types shown with IEEEG1 and
described in the 2013 IEEE PES Governor Report
The type 1 is an intentional deadband, implemented to
prevent excessive response
– Until the deadband activates there is no response, then
normal response after that; this can cause a potentially
large jump in the response
– Also, once activated there is normal
response coming back into range
– Used on input to IEEEG1
5
Deadbands
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The type 2 is also an intentional deadband,
implemented to prevent excessive response
– Difference is response does not jump, but rather only starts
•
once outside of the range
Another type of deadband is the
unintentional, such as will occur
with loose gears
– Until deadband "engages"
there is no response
– Once engaged there is
a hysteresis in the
response
6
Deadband Example: ERCOT
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•
Prior to November 2008, ERCOT required that the
governor deadbands be no greater than +/- 0.036 Hz
After 11/3/08 deadbands were changed to +/- 0.0166 Hz
ERCOT Frequency Profile Comparison
525,600 One Minute Periods per Year
45000
One Minute Occurances
40000
35000
30000
25000
20000
15000
10000
2008 did
have
two
months
with the
lower
values
5000
60
60
.0
1
60
.0
2
60
.0
3
60
.0
4
60
.0
5
60
.0
6
60
.0
7
60
.0
8
60
.0
9
60
.1
59
.9
59
.9
1
59
.9
2
59
.9
3
59
.9
4
59
.9
5
59
.9
6
59
.9
7
59
.9
8
59
.9
9
0
2009
2008
Image Source: Sydney Niemeyer, NRG, 2/9/10 presentation to Texas Regional Entity (part of ERCOT)
7
Gas Turbines
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A gas turbine (usually using natural gas) has a
compressor, a combustion chamber and then a turbine
The below figure gives an overview of the modeling
HRSG is
the heat
recovery
steam
generator
(if it is a
combined
cycle unit)
Image from IEEE PES, "Dynamic Models for Turbine-Governors in Power System Studies," Jan 2013
8
GAST Model
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Quite detailed gas turbine models exist; we'll just
consider the simplest, which is still used some
It is somewhat similar
to the TGOV1. T1 is for
the fuel valve, T2
is for the turbine, and
T3 is for the load
limit response based
on the ambient
temperature (At);
T3 is the delay in
measuring the exhaust
temperature
9
Play-in (Playback) Models
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Often time in system simulations there is a desire to test
the response of units (or larger parts of the simulation)
to particular changes in voltage or frequency
– These values may come from an actual system event
"Play-in" or playback models can be used to vary an
infinite bus voltage magnitude and frequency, with data
specified in a file
PowerWorld allows both the use of files (for say
recorded data) or auto-generated data
– Machine type GENCLS_PLAYBACK can play back a file
– Machine type InfiniteBusSignalGen can auto-generate a
signal
10
PowerWorld Infinite Bus
Signal Generation
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Below dialog shows some options for auto-generation
of voltage magnitude and frequency variations
Start Time tells when to start; values are
then defined for up to five separate time
periods
Volt Delta is the magnitude of the pu
voltage deviation; Volt Freq is the
frequency of the voltage deviation in Hz
(zero for dc)
Speed Delta is the magnitude of the
frequency deviation in Hz; Speed Freq is
the frequency of the frequency deviation
Duration is the time in seconds for the
time period
11
Example: Step Change Voltage
Response
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Below graph shows the voltage response for the four
bus system for a change in the infinite bus voltage
1.125
1.12
1.115
1.11
1.105
1.1
1.095
1.09
1.085
1.08
1.075
1.07
1.065
1.06
1.055
1.05
1.045
1.04
1.035
1.03
1.025
1.02
1.015
1.01
1.005
1
0
1
2
3
b
c
d
e
f
g
4
5
V (pu)_Bus Bus 2 g
b
c
d
e
f
6
7
8
9
10
V (pu)_Bus Bus 4
Case name: B4_SignalGen_IEEEG2
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Simple Diesel Model: DEGOV
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Sometimes models implement time delays (DEGOV)
– Often delay values are set to zero
Delays can be implemented either by saving the input
value or by using a Pade approximation, with a 2nd
order given below; a 4th is common
e
 sTD
1  k1 s  k2 s
TD

, k1  , k2 
2
1  k1 s  k2 s
2
12
2
TD2
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DEGOV Delay Approximation
With TD set to 0.5 seconds (which is longer than normal
in order to illustrate the delay)
Transient Stability Tim e Step Results Variables
1.2
1.19
1.18
1.17
1.16
1.15
1.14
1.13
1.12
Values
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1.11
1.1
1.09
1.08
1.07
1.06
1.05
1.04
1.03
1.02
1.01
1
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 3 3.2 3.4 3.6 3.8 4 4.2 4.4 4.6 4.8 5
Time
Gen Bus 4 #1 States of Governor\Actuator 3
Gen Bus 4 #1 Other Fields of Governor\Engine
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Hydro Units
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Hydro units tend to respond slower than steam and gas
units; since early transient stability studies focused on
just a few seconds (first or second swing instability),
detailed hydro units were not used
– The original IEEEG2 and IEEEG3 models just gave the linear
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response; now considered obsolete
Below is the IEEEG2; left side is the governor, right
side is the turbine and water column
For sudden changes
there is actually an
inverse change in
the output power
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Four Bus with an IEEEG2
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Graph below shows the mechanical power output of
gen 2 for a unit step decrease in the infinite bus
frequency; note the power initially goes down!
175
60
170
59.95
165
160
155
150
145
59.8
59.75
140
59.7
135
59.65
130
59.6
125
59.55
120
59.5
115
59.45
110
105
100
95
90
Physically this is
caused by a transient
decrease in the water
pressure when the
valve is opened to
increase the water
flow
59.9
59.85
59.4
59.35
59.3
59.25
85
59.2
80
59.15
75
59.1
70
59.05
65
59
0
1
2
b
c
d
e
f
g
3
4
Speed_Gen Bus 2 #1
5
b
c
d
e
f
g
6
7
8
9
10
Mech Input_Gen Bus 4 #1
Case name: B4_SignalGen_IEEEG2
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IEEEG3
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This model has a more detailed governor model, but the
same linearized turbine/water column model
Because of the initial inverse power change, for fast
deviations the droop value is transiently set to a larger
value (resulting in less of a power change)
WECC has
about 10% of
their governors
modeled with
IEEEG3s
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Washout Filters
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A washout filter is a high pass filter that removes the
steady-state response (i.e., it "washes it out") while
passing the high frequency response
sTw
1  sTw
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They are commonly used with hydro governors and (as
we shall see) with power system stabilizers
With hydro turbines ballpark values for Tw are around
one or two seconds
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IEEEG3 Four Bus Frequency Change
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The two graphs compare the case response for the
frequency change with different Rtemp values
60
107
106.5
106
105.5
105
104.5
104
103.5
60
59.95
117
59.9
116
59.85
115
114
59.8
113
59.75
112
59.7
59.65
59.95
59.9
59.85
59.8
59.75
111
59.7
110
59.65
103
59.6
109
59.6
102.5
59.55
108
59.55
102
59.5
107
59.5
101.5
59.45
106
59.45
101
59.4
105
59.4
100.5
59.35
104
59.35
100
59.3
103
99.5
59.25
102
59.2
101
99
98.5
98
97.5
97
100
59.15
99
59.1
98
59.05
97
59
59.3
59.25
59.2
59.15
59.1
59.05
59
0
1
2
b
c
d
e
f
g
3
4
5
Speed_Gen Bus 2 #1
b
c
d
e
f
g
6
7
8
9
Mech Input_Gen Bus 4 #1
Rtemp = 0.5, Rperm = 0.05
10
0
1
2
b
c
d
e
f
g
3
4
Speed_Gen Bus 2 #1
5
b
c
d
e
f
g
6
7
8
9
10
Mech Input_Gen Bus 4 #1
Rtemp = 0.05, Rperm = 0.05
Case name: B4_SignalGen_IEEEG2
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Basic Nonlinear Hydro Turbine Model
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Basic hydro system is shown below
– Hydro turbines work be converting the kinetic energy in the
water into mechanical energy
– assume the water is incompressible
At the gate assume a velocity of U, a cross-sectional
penstock area of A; then the
volume flow is A*U=Q;
Source: 9.2, Kundur, Power System Stability and Control, 1994
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Basic Nonlinear Hydro Turbine Model
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From Newton's law
dQ
L
 Fnet  A g  H  H gate  H loss 
dt
where  is the water density, g is the gravitational constant,
H is the static head (at the drop of the reservoir) and H gate is
the head at the gate (which will change as the gate position is
changed) and H loss is the head loss due to friction in the penstock
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As per [a] paper, this equation is normalized to
dq

dt
1  hgate  hloss 
TW
T is called the water time
constant, or water
starting time
[a] "Hydraulic Turbine and Turbine Control Models for System Dynamic Studies," IEEE Trans. Power Syst., Feb, 92
21
Basic Nonlinear Hydro Turbine Model
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With hbase the static head, qbase the flow when the gate is
fully open, an interpretation of Tw is the time (in
seconds) taken for the flow to go from stand-still to full
flow if the total head is hbase
If included the head losses, hloss, vary with the square of
the flow
The flow is assumed to vary as linearly with the gate
position (denoted by c)
q
q  c h or h   
c
2
22
Basic Nonlinear Hydro Turbine Model
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Power developed is proportional to flow rate and head,
with a term qnl added to model the fixed turbine (no
load) losses
– The term At is used to change the per unit scaling to that of
the electric generator
Pm  At h  q  qnl 
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Model HYGOV
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This simple model, combined with a governor, is
implemented in HYGOV
About
10% of
WECC
governors
use this
model
Hloss is assumed small and not included
The gate position (gv) to gate power (pgv)
is sometimes represented with a nonlinear curve
24
Linearized Model Derivation
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The previously
mentioned
linearized model
can now be
derived as
dq  1  h(c) gate 

dt
TW
h(c) gate
d q
q
q

 q 
c  h
dt
TW
c
h
And for the linearized power
Pm
Pm
Pm 
h 
q
h
q
 q Pm
Pm q 
 sTw

h c 
Pm  c q
Then

q
c
1  sTw
h
25
Four Bus Case with HYGOV
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The below graph plots the gate position and the power
output for the bus 2 signal generator decreasing the
speed then increasing it
Note that just
like in the
linearized
model, opening
the gate
initially
decreases the
power output
0.96
0.955
0.95
112
111
110
0.945
109
0.94
108
0.935
0.93
0.925
0.92
0.915
107
106
105
104
103
0.91
102
0.905
101
0.9
100
0.895
99
0.89
98
0.885
97
0
1
2
3
g
b
c
d
e
f
b
c
d
e
f
g
4
5
6
7
8
9
10
Mech Input_Gen Bus 4 #1
States of Governor\Gate_Gen Bus 4 #1
26
PID Controllers
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•
Governors and exciters often use proportional-integralderivative (PID) controllers
PIDs combine
– Proportional gain, which produces an output value that is
proportional to the current error
– Integral gain, which produces an output value that varies with
the integral of the error; this will eventually drive the error to
zero
– Derivative gain, which acts to predict the system behavior.
This can enhance system stability, but it can be quite
susceptible to noise
27
PID Example: Position Control
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•
•
•
Say we wish to get an object to a position in 1dimensional space by controlling its acceleration (force)
– Error is distance from desired position
– Control is speed
With just proportional control, acceleration will be
decreasing, but we'd reach maximum speed at the
desired point, overshooting
With derivative control, we'll be slowing down,
avoiding the overshoot
The integral term will make sure we stay at the desired
point
28
HYG3
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The HYG3 models either a PID or a double derivative
Looks more
complicated
than it is
since
depending
on cflag
only one of
the upper
paths is
used
29